The Royal Family are said to be "hurt" at the Duke and Duchess of Sussex's announcement they will step back as senior royals.
Prince Harry and Meghan did not consult any senior royal before making the statement, the BBC understands.
Buckingham Palace was "blindsided", said BBC royal correspondent Jonny Dymond, as talks about their future had begun but were in very early stages.
The Palace said there were "complicated issues" to work through.
In their statement on Wednesday, Harry and Meghan said they made the decision "after many months of reflection and internal discussions".
They said they intend "to step back as 'senior' members of the Royal Family, and work to become financially independent".
They plan to split their time between the UK and North America, while "continuing to honour our duty to the Queen, the Commonwealth, and our patronages".
"This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter," the couple said.
The pair was already preparing to launch their own Sussex Royal charity, which they set up after splitting from the Duke and Duchess of Cambridge's foundation in June last year.
The Sussexes' new charity is expected to be global, linked to Africa and the US, rather than domestic - and will have a commitment to female empowerment.
The couple's announcement raises numerous questions over what their future royal roles will entail.